Preheat oven to 375 degrees. In a mixing bowl, whisk the flour, 1/2 cup sugar, baking powder, and salt together; set aside. Grease a 9x13-inch baking dish. Beat the egg, butter, and milk in a bowl until smooth. Stir in the flour mixture until moistened, then spread into baking dish. Stir together the rhubarb, 2 cups of sugar, and water; pour over flour mixture in baking dish. Bake until the dough has set, about 50 minutes.